Paper 2021/1007
Provably Solving the Hidden Subset Sum Problem via Statistical Learning
Jean-Sebastien Coron and Agnese Gini
Abstract
At Crypto '99, Nguyen and Stern described a lattice based algorithm for solving the hidden subset sum problem, a variant of the classical subset sum problem where the $n$ weights are also hidden. As an application, they showed how to break the Boyko et al. fast generator of random pairs $(x,g^x \pmod{p})$. The Nguyen-Stern algorithm works quite well in practice for moderate values of $n$, but its complexity is exponential in $n$. A polynomial-time variant was recently described at Crypto 2020, based on a multivariate technique, but the approach is heuristic only. In this paper, we describe a proven polynomial-time algorithm for solving the hidden subset-sum problem, based on statistical learning. In addition, we show that the statistical approach is also quite efficient in practice: using the FastICA algorithm, we can reach $n=250$ in reasonable time.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- Hidden subset-sum problemlattice attackstatistical attack
- Contact author(s)
-
jscoron @ gmail com
agnese gini @ uni lu - History
- 2021-08-03: received
- Short URL
- https://ia.cr/2021/1007
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2021/1007,
author = {Jean-Sebastien Coron and Agnese Gini},
title = {Provably Solving the Hidden Subset Sum Problem via Statistical Learning},
howpublished = {Cryptology {ePrint} Archive, Paper 2021/1007},
year = {2021},
url = {https://eprint.iacr.org/2021/1007}
}
